Advertisements
Advertisements
Question
Express the following decimal as a rational number.
17.027
Advertisements
Solution
Let x = 17.027
= 17.027777..
Here, only number 7 is being repeated, so first we need to remove 02 which proceeds 7.
We multiply by 100 so that only the recurring digits remain after decimal.
∴ 100x = 1702.7777.... ....(1)
The number of digits recurring in equation (1) is 1, so we multiply both sides of the equation (1) by 10.
∴ 1000x = 10 x 1702.7777....
= 17027.7774..... ....(2)
On subtracting (1) from (2), we get
900x = 15325
∴ x = `(15325)/(900)`
= `(613)/(26)`
∴ 17.027 = `(613)/(36)`
APPEARS IN
RELATED QUESTIONS
Write the following number in `bb("p"/"q")` form.
29.568
Write the following rational number in decimal form.
`(-103)/5`
Write the numerator of the following rational numbers: `(- 125)/127`
Separate positive and negative rational numbers from the following:
`(-3)/5 , 3/-5 , (-3)/(-5), 3/5 , 0 , (-13)/-3 , 15/-8 , (- 15)/8`
The sum of two numbers is `- 6/5`. If one of them is -2, find the other.
What should be added to `(-7)/12` to get `3/8`?
State if the following fraction has a terminating decimal
`(37)/(40)`
State if the following fraction has a terminating decimal.
`(147)/(160)`
Express the following decimal as a rational number.
4.6724
Write the decimal form of the following rational numbers
`(-18)/7`
